Theoretical investigation of quadrupole contributions to surface sum-frequency vibrational spectroscopy

We study the effect of electric transition quadrupole moments on surface sum-frequency vibrational spectroscopy (SFVS). The SSP, PPP and SPS effective sum-frequency susceptibilities are derived from the nonzero macroscopic susceptibility tensors and related to molecular quadrupole polarizabilities. Using time-dependent density functional theory, we calculate the quadrupole susceptibilities of R-limonene liquids for the first time. The results indicate that quadrupole contributions have a significant influence on SFVS transmitted signals in the SPS polarization combination. We also suggest that the SPS spectra may be used as a general technique for detecting electric transition quadrupole moments.